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Talking Point

The heat is on

With climate change threatening to melt the world’s
ice sheets and cause devastating flooding, glaciologists
have their work cut out for them, explain Tavi Murray,
Ian Rutt and David Vaughan.

Planes travelling from Europe to the west coast of the
US usually fly directly over Greenland. Most passengers
miss it, but if you have a window seat and keep
watch at about the time that the dinner trays are being
cleared away, then you may be lucky enough to catch a
glimpse of a truly majestic landscape in which massive
glaciers, fed from a vast and featureless ice sheet, spill
into iceberg-choked fjords. Although your plane will
be thousands of metres overhead, these remote glaciers
are nonetheless feeling the impact of human activities
like air travel. As the temperatures over Greenland rise
as a result of climate change, the speed at which many
of these glaciers are moving is increasing so rapidly that
more ice is being lost from the ice sheet than is being
replaced by new snowfall. In other words, the ice sheet
is giving up its mass to the oceans, and, as a result, sea
levels are rising.

The rate of sea-level rise has startled both scientists
and policy-makers enough to make headlines and
become embedded in government and international
reports. It is easy to see why they are concerned – even
a half-metre rise would cause flooding that would affect
hundreds of millions of people in low-lying areas.
Suddenly, "glacier dynamics" – the physics that controls
how fast glaciers flow – has become a subject of
international importance.

The 2007 report from the Intergovernmental Panel
on Climate Change (IPCC) cites retreating glaciers and
rising sea levels as evidence that warming of the climate
system is unequivocal. And with enough water stored in
the Greenland and Antarctic ice sheets to raise global
sea levels by approximately 7 m and 57 m, respectively,
being able to predict how these large ice sheets will
behave in a warming climate is critical if we are fully to
understand the consequences of climate change.

We know from satellite measurements and an international
network of tide gauges that sea levels are currently
rising at a rate of slightly more than 3mm per
year. About half of this increase is due to the loss of ice
from glaciers and ice sheets, with the remainder being
caused by thermal expansion as the oceans warm. This
rate is higher now than at any point in the past century
and continued climate warming means that it is highly
likely to increase further in the future. Using a linear
extrapolation of data from the past 100 years, Stefan
Rahmstorf at the Potsdam Institute for Climate Research
in Germany last year showed that sea levels will
rise by 0.5–1.4m over the next 100 years. But, as NASA
climate scientist James Hansen has pointed out, the
data from the last 100 years do not include much contribution
from the ice sheets. The impact of these ice
sheets melting is sure to be felt more and more over the
next century.

Ice in motion

Glacier flow was first measured scientifically in the
early 19th century by Franz Josef Hugi, who was a physicist
and natural historian at Solothurn University of
Applied Sciences in Switzerland. Using simple visual
methods to study the position of a rock on the surface
of a glacier in the Alps, Hugi found that it moved by a
total of about 1300 m over a nine-year period between
1827 and 1836. By the early 1840s, the Swiss–American
geologist Louis Agassiz and the Scottish physicist James Forbes were also studying alpine glaciers. One
of Forbes’s most significant findings came in 1842 when
he reported results from theodolite surveys that
showed that the flow rate of glaciers is not constant but
varies from day to day and from week to week. Measurement
techniques have continued to improve since
then and, thanks to the advent of satellites and the
Global Positioning System (GPS), we have now discovered
a vast richness of glacier behaviour.

On a typical mountain glacier, snow is added to the
surface during the winter, while the snow and exposed
ice on the lower part of the glacier (known as the ablation
zone) melts during the summer. However, further
up the glacier, in the region known as the accumulation
zone, the snow remains year round and is converted
into ice as the load from the snow above it increases.
For a glacier to stay in equilibrium (i.e. for the amount
of water it contains to stay constant), the accumulation
zone needs to comprise about 70% of the total area of
the glacier.

If a glacier in equilibrium were not flowing, the ablation
zone would get thinner and the accumulation zone
would thicken, so overall the glacier would become
steeper. A certain amount of flow, therefore, is required
to maintain the geometry of a glacier in equilibrium.
Recognizing these concepts allows us to
calculate any glacier or ice sheet’s "balance velocity" –
a theoretical concept that defines how fast any glacier
needs to flow in order to retain the same shape and
volume. If a glacier is flowing faster than the balance
velocity, then it will thin; whereas if the glacier is flowing
more slowly, then it will thicken.

We now know that there are three processes by
which glaciers can flow. The first is viscous deformation
of the ice itself, which depends on many factors,
particularly temperature. A glacier can also slide over
the rock or sediment bed beneath it. Finally, the sediment
beneath a glacier can deform, thus carrying forward
the ice resting on it. The rates of both sliding and
sediment deformation are affected most by the presence
of pressurized water at the glacier bed, since this
reduces friction. This water can reach the glacier bed
when surface meltwater enters the glacier through vertical
shafts known as moulins, which form when water
flows down into and so enlarges cracks or crevasses in
the ice. Once water is flowing inside the glacier, it often reaches the glacier bed, where it flows in channels.

Sometimes the amount of water reaching the glacier
bed can increase significantly – for example when
melting begins at the start of summer, or when a surface
lake drains. (Sudden drainage is a feature of icedammed
lakes, since the ice can deform, be melted, be
cut by flowing water or overtopped by rising lake levels.)
When this occurs, the pressure of the water at the
glacier bed can get quite high and so make the glacier
flow significantly faster. This process explains the
short-term variations in glacier speed that Forbes saw
in the Alps.

Space-age measures

These days we can measure glacier flow rates much
more widely than in Forbes’s time by using satellites
such as the US Landsat series and the European Space
Agency’s Envisat and ERS satellites. Indeed, such
measurements are vital for monitoring the remote
parts of ice sheets that have never, or only very rarely,
been visited. Features such as crevasses on the ice surface
can be automatically tracked over a period of time
with either optical imagery from satellites that passively
detect reflected solar radiation, or via synthetic aperture
radar (SAR) microwave radiation that is actively
transmitted by the satellite. As SAR provides its own
illumination, it has the advantage of not being affected
by clouds and can be used during the polar night.

By comparing two SAR images of the same surface
obtained at different times, we can also map the topography
and dynamics of a glacier or ice sheet using interferometry.
This technique exploits the phase shift
between the transmitted and backscattered SAR signals.
If the same viewing location is used and the surface
characteristics have not altered, then the phase
difference depends only on the displacement of the surface.
If, however, the viewing location changes, which is
usually the case between two satellite passes, then the
phase difference also depends on the local topography.
Using interferometry we can therefore estimate not
only flow rates but changes in ice thickness, too.

Satellite measurements could, in principle, be used to monitor almost all of the Earth’s ice masses. However,
they are limited in temporal resolution because a
satellite takes time to orbit the Earth and may only pass
over the same point every few weeks at best. The
shorter-term variations in ice flow, such as those reported
by Forbes, are now usually measured by attaching
GPS receivers to glaciers, which allows position to
be measured to better than a few centimetres (see
Physics World October :2007 pp34–38).

These techniques have revealed that glacier flow
rates vary by several orders of magnitude: from a sluggish
few metres per year, as seen in glaciers with cold
bases such as Austre Brøggerbreen on Svalbard in the
Arctic Ocean, to sustained flow rates of about 8-10 km
per year. Jakobshavn Isbrae in Greenland used to be
considered the fastest flowing glacier with a flow rate
of about 8.3 km per year, but researchers now routinely
measure velocities of 7-10 km per year for most Greenland
outlet glaciers. Furthermore, recent observations
by many different research groups show dramatic variations
both spatially and temporally, which suggest that
flow rates are very sensitive to local glaciologic, geologic
and climatic conditions.

Particularly large spatial variations in flow rates occur
within ice sheets. Most parts of the Antarctic ice sheet,
for example, flow relatively slowly at only a few metres
per year, but some areas move much faster at about
400 m per year or more. These variations are caused by
changes in the resistive stresses at the bed of the ice,
which occur due to changes in the temperature and the
water system at the base, and the presence of wet sediments
beneath the ice. Changes in the driving stress –
primarily the surface slope – also play a part. These fast
flow features, known as ice streams, constitute only
about 10% of the Antarctic coastline but discharge
about 90% of the snow that accumulates and so act to
regulate the storage of water in the ice sheet.

Large temporal variations in flow have been observed
both on ice sheets and on mountain glaciers. In
Antarctica, ice streams have both sped up (discharging
more ice to the oceans) and slowed down or stopped
(reducing the discharge of ice), while an even more
dramatic temporal variation is seen in "surge-type"
glaciers. These glaciers lie quiescent for decades or
longer before their flow rates suddenly increase by up
to three orders of magnitude, allowing them to advance
very rapidly. During its surges in 1982 and 1983, the
Variegated Glacier in Alaska, for example, flowed up
to 2.6 m per hour for a few hours, while the Hispar
Glacier in the Karakoram Himalayas advanced 3.2 km
in eight days during a surge event.

What is most intriguing about these surge-type glaciers
is that they alternate between fast and slow flow
in cycles that are thought to be largely independent of
climate. During the slow phase of flow, the upper part
of a surge-type glacier accumulates more snow than is
lost and the glacier thickens and steepens, which increases
the shear stress at the glacier bed. Eventually
this increase in stress crosses a threshold and a surge is
triggered. There are a number of competing theories
as to what changes at the bed between the quiescent
and fast-flow states, but all of these models involve the
entrapment of high-pressure water at the bed, which
reduces basal friction.

Breaking the ice

Other types of glacier, however, have been significantly
affected by climate warming. In 2002 in the Antarctic,
during the space of just a few weeks, the Larsen B Ice
Shelf, which spanned an area of 1600 km2, collapsed.
Before it broke up, air temperatures had reached record
levels and satellite images showed lakes of meltwater
on the ice shelf. This event did have one useful
consequence, however. An ice shelf forms where a glacier
or ice sheet flows down to a coastline and onto the
ocean surface, and glaciologists had long debated how
much back-stress the floating ice shelf provides to the
glaciers that feed it and how much those glaciers would
therefore be affected by removal of the ice shelf. The
loss of Larsen B allowed them to find out.

Satellite feature tracking showed that the glaciers
that had fed Larsen B started flowing twice to six times
as fast after the ice shelf collapsed, whereas nearby
glaciers that fed an intact region of the ice shelf did not
change their speed. So, while the ice-shelf collapse
itself did not raise sea levels because it was already
floating, the increased flow rates of the glaciers that fed
it led to greater discharge into the oceans, causing sea
levels to rise.

In Greenland, temperatures are generally warmer
than those in Antarctica and substantial areas of the
ice sheet melt each summer – indeed melting accounts
for half of the loss in the mass of the ice sheet. Most of
the Greenland ice sheet terminates on land and measurements
obtained using GPS receivers have shown
that flow at the land-based margin of the ice sheet
speeds up between 5-25% in periods of strong surface
melting – just like the glaciers Forbes studied in the
Alps. This makes it clear that the meltwater is efficiently
transported to the ice-sheet bed even through
thick ice.

The other half of the mass lost breaks off as icebergs
from fast-flowing outlet glaciers, which discharge into
deep fjords. Observations made in 2004 by a team led
by NASA glaciologist Bill Krabill using airborne altimetry
– a technique for mapping the topography of
the ground using a laser flown on a plane – have shown
significant thinning of some of these outlet glaciers at
rates of more than 10m per year. Satellite observations
have shown that many have also greatly increased their
flow rates, especially in south-east Greenland. This
acceleration in flow increases the glacier’s mass loss to
the oceans and hence contributes to rises in sea levels.

Two of these outlet glaciers, the Helheim and Kangerdlugssuaq
glaciers on the south-east coast of Greenland,
simultaneously retreated by more than 5 km in
spring 2004 while approximately doubling their flow
rates and the volume of ice calved. A third glacier,
Jakobshavn Isbrae, had similarly sped up a few years
previously, after many years of stable flow.

These large changes in flow rates were a surprise to
glaciologists and cannot be reproduced by current theories
of glacier dynamics. They are almost certainly the
result of increased air or ocean temperatures, although
"tidewater glaciers" (which terminate in a fjord or the
sea) do have a known cycle of advance and retreat. It
is possible, therefore, that the changes observed in
Greenland are part of a natural cycle. But it would certainly
be surprising that so many glaciers are accelerating and retreating simultaneously if no external forcing
were occurring. Without such forcing, one would
expect some glaciers to advance while others retreat.

Model behaviour

Predicting the future contribution of glaciers and ice
sheets to sea-level rises has become one of the most
important goals of glacier studies, since such information
is essential for planning sea-defences and adapting
to sea-level rises. This is far from easy, however.
We have too few records of the glacial response to climate
change to build a statistical approach to prediction,
and even the smallest glacier is too large on
which to conduct a controlled experiment. Glaciologists
therefore have to base their predictions on the
results of numerical models.

Such models must balance increasing complexity
against increasing computational cost. More complex
models should be more accurate because the physics
included in them is more advanced and because they
have many more data points to improve the model’s
spatial and temporal resolution. However, complex
models can take a long time to run, which means that
they are only used for short-term simulations of smaller glaciers. Where we are interested in the longer-term
evolution of a large ice sheet, a lower-resolution model,
including only a few key parameters, has to be used.

The simplest models represent 2D vertical slices
though the ice, aligned along lines of flow, and consider
the ice to be the same temperature throughout. The
modelled quantities are ice-surface elevation and flow
speed, while the ice temperature (which affects the
softness of the ice), the properties of the bed (such as its
elevation and the presence or absence of sliding), and
the surface-mass balance (i.e. melting or accumulation)
are the controlling parameters. The ice flow is assumed
to be laminar so that only vertical gradients in the horizontal
shear stresses need to be included – this is the
shallow-ice approximation, which is based on the
assumption that the horizontal extent of an ice mass is
much larger than its thickness. This approximation is
good for most parts of a large ice sheet, but is inappropriate for fast-flowing ice streams or for valley glaciers.

At the other end of the spectrum, the most complex
models include representations of the additional stress
gradients (termed higher-order stresses) and are also
able to compute the 3D temperature field. Both of
these aspects are essential for the representation of ice
streams and outlet glaciers, and so are critical to an understanding of the Greenland and Antarctic ice sheets.

In recent years, a number of such higher-order
models have been developed, by, among others, Frank
Pattyn at Vrije Universiteit in Brussels, and Fuyuki
Saito and co-workers at the University of Tokyo. These
models are opening up exciting possibilities in the study of smaller-scale motion in ice sheets, but they do have
their limitations. In particular, the bed of the ice sheet
or glacier is of critical importance but current models
make simple assumptions about this basal sliding
rather than attempting to represent the full range of
processes involved. In order to improve the numerical
models, therefore, our understanding of the physics of
basal sliding and the water systems that form at the
beds of glaciers needs to be improved and generalized.
To this end, much more information is needed about
the basal conditions of particular ice masses.

This presents a difficult challenge, since the bed of
an ice sheet or glacier is the hardest part to observe. A
few access holes have been drilled through ice more
than a kilometre thick using jets of high-pressure hot
water, and Barclay Kamb and Herman Englelhardt’s
group at the California Institute of Technology in the
US has measured the pressure of basal water and the
rates of sliding and sediment deformation through
these holes. Borehole cameras have also revealed cavities
full of water beneath an ice stream. Even when
access can be achieved, however, spatial sampling is
very small since the boreholes are typically less than
15 cm in diameter.

Geophysical techniques allow much greater areas
to be covered, and indeed seismic and radar surveys,
which were both originally used simply to measure the
thickness of glaciers, have been highly successful in determining basal conditions. Seismic-reflection surveys
use acoustic energy to map the impedance contrast
across the basal interface. Rock and sediments that are not deforming are acoustically harder than ice, whereas
deforming sediments are acoustically softer, so the
reflection coefficient of the acoustic waves changes
depending on whether the ice is sliding over hard sediments
or moving with deforming soft sediments.

Radar, on the other hand, uses pulses of highfrequency
electromagnetic radiation (at about 10-200 MHz). Since radar reflections from water are short in duration and high in amplitude, whereas soft sediments or rough bedrock produce longer and lower amplitude pulses, radar can be used to map the occurrence of water at the glacier bed, including the presence
of sub-ice lakes. Radar systems can be mounted
on an aircraft allowing very large areas of the bed to be
surveyed, which is critical if ice-sheet models are to
incorporate more basal physics. Used together, borehole
and geophysical techniques have enormous potential
to map the topography, basal environments and
water systems of the major ice masses.

On thin ice

As observation technology improves, it is revealing an
amazing richness of glacial behaviours. At present,
however, most of this dynamic richness cannot be reproduced
by models. An unfortunate result of this situation
is that in its report last year, the IPCC said that
its predictions of future sea-level rise have excluded
future rapid dynamical changes in ice flow because "a
basis in published literature is lacking". This limits our
confidence in the predictions and hampers the ability of governments to draw up plans for dealing with the future
consequences of climate change. Furthermore, the
report’s predictions of 0.18-0.59 m rises are as a result
most likely lower-limit scenarios.
In the worst-case scenario, in which all of the world’s
ice melts, sea levels would rise by over 65 m. Some 57 m
would come from Antarctica, 7 m from Greenland and
between 0.15 and 0.37 m from small glaciers. While this
extreme case is unlikely, even a small rise in sea levels
would have a devastating effect on millions of people,
and could see large areas of land disappearing under
water. To provide better confidence in calculated rates
of future sea-level rises and begin preparing for them,
significant further research is needed in the form of
both improved modelling efforts and continued field
and satellite observation.

About the author

Tavi Murray and Ian Rutt are in the Glaciology Group in the School of the Environment and Society at Swansea University, UK, and David Vaughan is in the British Antarctic Survey.
This article originally appeared in the May issue of PhysicsWorld.